Yakov M. Shnir 
Magnetic Monopoles 

“One would be surprised if Nature had made no use of it.” P.A.M. Dirac According to some dictionaries, one meaning of the notion of “beauty” is “symmetry”. Probably, beauty is not entirely “in the eye of the beholder”. It seemstoberelatedtothesymmetryoftheobject.Fromaphysicalviewpoint, this de?nition is very attractive: it allows us to describe a central concept of theoretical physics over the last two centuries as being a quest for higher symmetry of Nature. The more symmetric the theory, the more beautiful it looks. Unfortunately, our imperfect (at least at low-energy scale) world is full of nasty broken symmetries. This has impelled physicists to try to understand how this happens. In some cases, it is possible to reveal the mechanism of violationandhowthesymmetrymayberecovered;thenourpictureof Nature becomes a bit more beautiful. One of the problems of the broken symmetry that we see is that, while there are electric charges in our world, their counterparts, magnetic mo- poles, have not been found. Thus, in the absence of the monopoles, the s- metry between electric and magnetic quantities is lost. Can this symmetry be regained? In the history of theoretical physics, the hypothesis about the possible existence of a magnetic monopole has no analogy. There is no other purely theoretical construction that has managed not only to survive, without any experimental evidence, in the course of more than a century, but has also remained the focus of intensive research by generations of physicists.

Table des matières

Dirac Monopole.- Magnetic Monopole in Classical Theory.- The Electron-Monopole System:Quantum-Mechanical Interaction.- Topological Roots of the Abelian Monopole.- Abelian Monopole: Relativistic Quantum Theory.- Monopole in Non-Abelian Gauge Theories.- ’t Hooft-Polyakov Monopole.- Multimonopole Configurations.- SU(2) Monopole in Quantum Theory.- Monopoles Beyond SU(2) Group.- Monopoles and the Problem of Confinement.- Fermions in the Field of Non-Abelian Monopole and Rubakov—Callan Effect.- Supersymmetric Monopoles.- Construction of Supersymmetric Yang-Mills Theories.- Magnetic Monopoles in the N = 2 Supersymmetric Yang-Mills Theory.- Seiberg—Witten Solution of N = 2 SUSY Yang—Mills Theory.